Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Sub-per-cent determination of the brightness at the tip of the red giant branch in the Magellanic Clouds

Subjects

Abstract

The value of the Hubble constant as constrained by type Ia supernovae is directly tied to the zero point of the extragalactic distance scale, which is in turn set by the calibration of astrophysical distance indicators such as the tip of the red giant branch (TRGB). In this article, a calibration of the TRGB luminosity is determined in the Magellanic Clouds. Composite colour–magnitude diagrams are constructed for the Small and Large Magellanic Clouds using regions in which the TRGB could be unambiguously identified. As a result, a sub-per-cent measurement of the TRGB in the Clouds is determined. The I versus (V − I) relation of the TRGB is found to be consistent with a constant I magnitude over colours 1.45 < (VI)0 < 1.95 mag, and a shallow, quadratic curvature is confirmed when including more metal-rich (up to (VI)0 = 2.2 mag) tip stars into the fit, and is the preferred solution. This study’s TRGB measurements also constrain the three-dimensional tilt of the Large Magellanic Cloud as well as the distance between the Small and Large Clouds. Both findings are in agreement with the independent, geometric constraints derived from the detached eclipsing binaries and establish a better than 0.02 mag cross-consistency (1% in distance) between the latest detached eclipsing binary measurements, red clump reddening maps and the TRGB measurements of this study.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: TRGB measurement in the LMC.
Fig. 2: TRGB measurement in the SMC.
Fig. 3: Colour dependence of the I-band TRGB.
Fig. 4: Addressing disagreement over measuring the TRGB in the LMC.

Similar content being viewed by others

Data availability

All data used in this work are publicly accessible, including OGLE-III photometry (http://ogle.astrouw.edu.pl/cont/4_main/map/map.html), OGLE-IV reddening maps (http://ogle.astrouw.edu.pl/cgi-ogle/get_ms_ext.py), Gaia EDR3 astrometry (https://gea.esac.esa.int/archive/) and the Harris and Zaritsky SFH maps (https://cdsarc.unistra.fr/viz-bin/cat/J/AJ/138/1243).

References

  1. Di Valentino, E. et al. In the realm of the Hubble tension—a review of solutions. Class. Quantum Gravity 38, 153001 (2021).

    Article  ADS  Google Scholar 

  2. Abdalla, E. et al. Cosmology intertwined: a review of the particle physics, astrophysics, and cosmology associated with the cosmological tensions and anomalies. J. High Energy Astrophys. 34, 49–211 (2022).

    Article  ADS  Google Scholar 

  3. Riess, A. G. et al. A 2.4% determination of the local value of the Hubble constant. Astrophys. J. 826, 56 (2016).

    Article  ADS  Google Scholar 

  4. Jang, I. S. & Lee, M. G. The tip of the red giant branch distances to type Ia supernova host galaxies. V. NGC 3021, NGC 3370, and NGC 1309 and the value of the Hubble constant. Astrophys. J. 836, 74 (2017).

    Article  ADS  Google Scholar 

  5. Freedman, W. L. et al. The Carnegie–Chicago Hubble Program. VIII. An independent determination of the Hubble constant based on the tip of the red giant branch. Astrophys. J. 882, 34 (2019).

    Article  ADS  Google Scholar 

  6. Riess, A. G., Casertano, S., Yuan, W., Macri, L. M. & Scolnic, D. Large Magellanic Cloud Cepheid standards provide a 1% foundation for the determination of the Hubble constant and stronger evidence for physics beyond ΛCDM. Astrophys. J. 876, 85 (2019).

    Article  ADS  Google Scholar 

  7. Yuan, W., Riess, A. G., Macri, L. M., Casertano, S. & Scolnic, D. M. Consistent calibration of the tip of the red giant branch in the Large Magellanic Cloud on the Hubble Space Telescope photometric system and a redetermination of the Hubble constant. Astrophys. J. 886, 61 (2019).

    Article  ADS  Google Scholar 

  8. Reid, M. J., Pesce, D. W. & Riess, A. G. An improved distance to NGC 4258 and its implications for the Hubble constant. Astrophys. J. Lett. 886, L27 (2019).

    Article  ADS  Google Scholar 

  9. Freedman, W. L. et al. Calibration of the tip of the red giant branch. Astrophys. J. 891, 57 (2020).

    Article  ADS  Google Scholar 

  10. Jang, I. S. et al. The Carnegie–Chicago Hubble Program. IX. Calibration of the tip of the red giant branch method in the megamaser host galaxy, NGC 4258 (M106). Astrophys. J. 906, 125 (2021).

    Article  ADS  Google Scholar 

  11. Soltis, J., Casertano, S. & Riess, A. G. The parallax of ω Centauri measured from Gaia EDR3 and a direct, geometric calibration of the tip of the red giant branch and the Hubble constant. Astrophys. J. Lett. 908, L5 (2021).

    Article  ADS  Google Scholar 

  12. Anand, G. S. et al. The Extragalactic Distance Database: the color–magnitude diagrams/tip of the red giant branch distance catalog. Astron. J. 162, 80 (2021).

    Article  ADS  Google Scholar 

  13. Freedman, W. L. Measurements of the Hubble constant: tensions in perspective. Astrophys. J. 919, 16 (2021).

    Article  ADS  Google Scholar 

  14. Graczyk, D. et al. The Araucaria Project: an accurate distance to the late-type double-lined eclipsing binary OGLE SMC113.3 4007 in the Small Magellanic Cloud. Astrophys. J. 750, 144 (2012).

    Article  ADS  Google Scholar 

  15. Pietrzyński, G. et al. An eclipsing-binary distance to the Large Magellanic Cloud accurate to two per cent. Nature 495, 76–79 (2013).

    Article  ADS  Google Scholar 

  16. Graczyk, D. et al. The Araucaria Project. The distance to the Small Magellanic Cloud from late-type eclipsing binaries. Astrophys. J. 780, 59 (2014).

    Article  ADS  Google Scholar 

  17. Graczyk, D. et al. The late-type eclipsing binaries in the Large Magellanic Cloud: catalog of fundamental physical parameters. Astrophys. J. 860, 1 (2018).

    Article  ADS  Google Scholar 

  18. Pietrzyński, G. et al. A distance to the Large Magellanic Cloud that is precise to one per cent. Nature 567, 200–203 (2019).

    Article  ADS  Google Scholar 

  19. Graczyk, D. et al. A distance determination to the Small Magellanic Cloud with an accuracy of better than two percent based on late-type eclipsing binary stars. Astrophys. J. 904, 13 (2020).

    Article  ADS  Google Scholar 

  20. Nidever, D. L. et al. The lazy giants: APOGEE abundances reveal low star formation efficiencies in the Magellanic Clouds. Astrophys. J. 895, 88 (2020).

    Article  ADS  Google Scholar 

  21. Salaris, M. & Cassisi, S. Evolution of Stars and Stellar Populations (Wiley, 2005).

  22. Jang, I. S. & Lee, M. G. The tip of the red giant branch distances to type Ia supernova host galaxies. IV. Color dependence and zero-point calibration. Astrophys. J. 835, 28 (2017).

    Article  ADS  Google Scholar 

  23. Górski, M. et al. The Araucaria Project: multi-band calibrations of the TRGB absolute magnitude. Astron. J. 156, 278 (2018).

    Article  ADS  Google Scholar 

  24. Górski, M. et al. Empirical calibration of the reddening maps in the Magellanic Clouds. Astrophys. J. 889, 179 (2020).

    Article  ADS  Google Scholar 

  25. Skowron, D. M. et al. OGLE-ing the Magellanic system: optical reddening maps of the Large and Small Magellanic Clouds from red clump stars. Astrophys. J. Suppl. Ser. 252, 23 (2021).

    Article  ADS  Google Scholar 

  26. Nataf, D. M., Cassisi, S., Casagrande, L., Yuan, W. & Riess, A. G. On the color–metallicity relation of the red clump and the reddening toward the Magellanic Clouds. Astrophys. J. 910, 121 (2021).

    Article  ADS  Google Scholar 

  27. Cappellari, M. & Copin, Y. Adaptive spatial binning of integral-field spectroscopic data using Voronoi tessellations. Mon. Not. R. Astron. Soc. 342, 345–354 (2003).

    Article  ADS  Google Scholar 

  28. Schlegel, D. J., Finkbeiner, D. P. & Davis, M. Maps of dust infrared emission for use in estimation of reddening and cosmic microwave background radiation foregrounds. Astrophys. J. 500, 525–553 (1998).

    Article  ADS  Google Scholar 

  29. Schlafly, E. F. & Finkbeiner, D. P. Measuring reddening with Sloan Digital Sky Survey stellar spectra and recalibrating SFD. Astrophys. J. 737, 103 (2011).

    Article  ADS  Google Scholar 

  30. Soszyński, I. et al. The OGLE collection of variable stars. Classical Cepheids in the Magellanic system. Acta Astron. 65, 297–312 (2015).

    ADS  Google Scholar 

  31. Kim, S., Dopita, M. A., Staveley-Smith, L. & Bessell, M. S. H i shells in the Large Magellanic Cloud. Astron. J. 118, 2797–2823 (1999).

    Article  ADS  Google Scholar 

  32. Nikolaev, S. et al. Geometry of the Large Magellanic Cloud disk: results from MACHO and the Two Micron All Sky Survey. Astrophys. J. 601, 260–276 (2004).

    Article  ADS  Google Scholar 

  33. van der Marel, R. P. & Cioni, M.-R. L. Magellanic Cloud structure from near-infrared surveys. I. The viewing angles of the Large Magellanic Cloud. Astron. J. 122, 1807–1826 (2001).

    Article  ADS  Google Scholar 

  34. Cusano, F. et al. The VMC Survey—XLII. Near-infrared period–luminosity relations for RR Lyrae stars and the structure of the Large Magellanic Cloud. Mon. Not. R. Astron. Soc. 504, 1–15 (2021).

  35. Scowcroft, V. et al. The Carnegie Hubble Program: the distance and structure of the SMC as revealed by mid-infrared observations of Cepheids. Astrophys. J. 816, 49 (2016).

    Article  ADS  Google Scholar 

  36. Muraveva, T. et al. The VMC survey—XXVI. Structure of the Small Magellanic Cloud from RR Lyrae stars. Mon. Not. R. Astron. Soc. 473, 3131–3146 (2018).

    Article  ADS  Google Scholar 

  37. Da Costa, G. S. & Armandroff, T. E. Standard globular cluster giant branches in the (MI, (VI)0) plane. Astron. J. 100, 162 (1990).

  38. Bellazzini, M., Ferraro, F. R. & Pancino, E. A step toward the calibration of the red giant branch tip as a standard candle. Astrophys. J. 556, 635–640 (2001).

    Article  ADS  Google Scholar 

  39. Valenti, E., Ferraro, F. R. & Origlia, L. Red giant branch in near-infrared colour–magnitude diagrams—I. Calibration of photometric indices. Mon. Not. R. Astron. Soc. 351, 1204–1214 (2004).

    Article  ADS  Google Scholar 

  40. Rejkuba, M., Greggio, L., Harris, W. E., Harris, G. L. H. & Peng, E. W. Deep ACS imaging of the halo of NGC 5128: reaching the horizontal branch. Astrophys. J. 631, 262–279 (2005).

    Article  ADS  Google Scholar 

  41. Rizzi, L. et al. Tip of the red giant branch distances. II. Zero-point calibration. Astrophys. J. 661, 815–829 (2007).

    Article  ADS  Google Scholar 

  42. Salaris, M. & Girardi, L. Tip of the red giant branch distances to galaxies with composite stellar populations. Mon. Not. R. Astron. Soc. 357, 669–678 (2005).

    Article  ADS  Google Scholar 

  43. Udalski, A. The Optical Gravitational Lensing Experiment. Real time data analysis systems in the OGLE-III survey. Acta Astron. 53, 291–305 (2003).

    ADS  Google Scholar 

  44. Udalski, A., Kubiak, M. & Szymanski, M. Optical Gravitational Lensing Experiment. OGLE-2—the second phase of the OGLE project. Acta Astron. 47, 319–344 (1997).

    ADS  Google Scholar 

  45. Udalski, A. et al. The Optical Gravitational Lensing Experiment. BVI maps of dense stellar regions. II. The Large Magellanic Cloud. Acta Astron. 50, 307–335 (2000).

    ADS  Google Scholar 

  46. Udalski, A., Szymanski, M. K., Soszynski, I. & Poleski, R. The Optical Gravitational Lensing Experiment. Final reductions of the OGLE-III data. Acta Astron. 58, 69–87 (2008).

    ADS  Google Scholar 

  47. Udalski, A., Szymański, M. K. & Szymański, G. OGLE-IV: fourth phase of the Optical Gravitational Lensing Experiment. Acta Astron. 65, 1–38 (2015).

    ADS  Google Scholar 

  48. Udalski, A. et al. The Optical Gravitational Lensing Experiment. OGLE-III photometric maps of the Large Magellanic Cloud. Acta Astron. 58, 89–102 (2008).

    ADS  Google Scholar 

  49. Szymański, M. K. et al. The Optical Gravitational Lensing Experiment. OGLE-III photometric maps of the Galactic bulge fields. Acta Astron. 61, 83–102 (2011).

    ADS  Google Scholar 

  50. Soszyński, I. et al. The Optical Gravitational Lensing Experiment. The OGLE-III catalog of variable stars. IV. Long-period variables in the Large Magellanic Cloud. Acta Astron. 59, 239–253 (2009).

    ADS  Google Scholar 

  51. Soszyński, I. et al. The Optical Gravitational Lensing Experiment. The OGLE-III catalog of variable stars. XIII. Long-period variables in the Small Magellanic Cloud. Acta Astron. 61, 217–230 (2011).

    ADS  Google Scholar 

  52. Gaia Collaboration. The Gaia mission. Astron. Astrophys. 595, A1 (2016).

    Article  Google Scholar 

  53. Gaia Collaboration. Gaia Early Data Release 3. Summary of the contents and survey properties. Astron. Astrophys. 649, A1 (2021).

    Article  Google Scholar 

  54. Lindegren, L. et al. Gaia Early Data Release 3. The astrometric solution. Astron. Astrophys. 649, A2 (2021).

    Article  Google Scholar 

  55. Fabricius, C. et al. Gaia Early Data Release 3. Catalogue validation. Astron. Astrophys. 649, A5 (2021).

    Article  Google Scholar 

  56. Torra, F. et al. Gaia Early Data Release 3. Building the Gaia DR3 source list—cross-match of Gaia observations. Astron. Astrophys. 649, A10 (2021).

    Article  Google Scholar 

  57. Ulaczyk, K. et al. Photometric maps based on the OGLE-III Shallow Survey in the Large Magellanic Cloud. Acta Astron. 62, 247–268 (2012).

    ADS  Google Scholar 

  58. Hoyt, T. J. et al. The near-infrared tip of the red giant branch. II. An absolute calibration in the Large Magellanic Cloud. Astrophys. J. 858, 12 (2018).

    Article  ADS  Google Scholar 

  59. Pawlak, M. Period–luminosity–colour relation for early-type contact binaries. Mon. Not. R. Astron. Soc. 457, 4323–4329 (2016).

    Article  ADS  Google Scholar 

  60. Haschke, R., Grebel, E. K. & Duffau, S. New optical reddening maps of the Large and Small Magellanic Clouds. Astron. J. 141, 158 (2011).

    Article  ADS  Google Scholar 

  61. Choi, Y. et al. SMASHing the LMC: mapping a ring-like stellar overdensity in the LMC disk. Astrophys. J. 869, 125 (2018).

    Article  ADS  Google Scholar 

  62. Fitzpatrick, E. L. Correcting for the effects of interstellar extinction. Publ. Astron. Soc. Pac. 111, 63–75 (1999).

    Article  ADS  Google Scholar 

  63. Hatt, D. et al. The Carnegie–Chicago Hubble program. II. The distance to IC 1613: the tip of the red giant branch and RR Lyrae period–luminosity relations. Astrophys. J. 845, 146 (2017).

    Article  ADS  Google Scholar 

  64. Persson, S. E. et al. New Cepheid period–luminosity relations for the Large Magellanic Cloud: 92 near-infrared light curves. Astron. J. 128, 2239–2264 (2004).

    Article  ADS  Google Scholar 

  65. Monson, A. J. et al. Standard Galactic field RR Lyrae. I. Optical to mid-infrared phased photometry. Astron. J. 153, 96 (2017).

    Article  ADS  Google Scholar 

  66. Madore, B. F., Mager, V. & Freedman, W. L. Sharpening the tip of the red giant branch. Astrophys. J. 690, 389–393 (2009).

    Article  ADS  Google Scholar 

  67. Harris, J. & Zaritsky, D. The star formation history of the Large Magellanic Cloud. Astron. J. 138, 1243–1260 (2009).

    Article  ADS  Google Scholar 

  68. Weinberg, M. D. & Nikolaev, S. Structure of the Large Magellanic Cloud from 2MASS. Astrophys. J. 548, 712–726 (2001).

    Article  ADS  Google Scholar 

  69. van der Marel, R. P., Alves, D. R., Hardy, E. & Suntzeff, N. B. New understanding of Large Magellanic Cloud structure, dynamics, and orbit from carbon star kinematics. Astron. J. 124, 2639–2663 (2002).

    Article  ADS  Google Scholar 

  70. Rubele, S. et al. The VMC survey—XXXI: the spatially resolved star formation history of the main body of the Small Magellanic Cloud. Mon. Not. R. Astron. Soc. 478, 5017–5036 (2018).

    Article  ADS  Google Scholar 

  71. de Vaucouleurs, G. & Freeman, K. C. Structure and dynamics of barred spiral galaxies, in particular of the Magellanic type. Vistas Astron. 14, 163–294 (1972).

    Article  ADS  Google Scholar 

  72. Cioni, M. R. L., Habing, H. J. & Israel, F. P. The morphology of the Magellanic Clouds revealed by stars of different age: results from the DENIS survey. Astron. Astrophys. 358, L9–L12 (2000).

    ADS  Google Scholar 

  73. van der Marel, R. P. & Kallivayalil, N. Third-epoch Magellanic Cloud proper motions. II. The Large Magellanic Cloud rotation field in three dimensions. Astrophys. J. 781, 121 (2014).

    Article  ADS  Google Scholar 

  74. Ripepi, V. et al. The VMC survey—XXV. The 3D structure of the Small Magellanic Cloud from classical Cepheids. Mon. Not. R. Astron. Soc. 472, 808–827 (2017).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

I am indebted to W. L. Freedman for her invaluable support and tutelage throughout my graduate studies, as well as insightful comments on and discussions regarding this manuscript. A. Udalski and the OGLE Collaboration are acknowledged for making publicly available the photometry from their revelatory survey. I thank D. and J. Skowron for making publicly accessible their reddening maps of the MCs. I thank J. Harris and D. Zaritsky for making publicly available their SFH maps of the LMC. I am thankful for the frequent, fundamental insights of B. Madore. I am grateful to H.-W. Chen for heartening and encouraging discussions. I thank R. Beaton for stimulating discussions regarding the Clouds. I highlight the work of M. Seibert who introduced the use of Voronoi tessellation to study resolved stellar populations, an approach that has since become common in the literature. I thank I. S. Jang for helpful comments and clarifications. I acknowledge M. Karouzos for helpful comments and suggestions. I thank C. Esmerian for his helpful comments. This work has made use of data from the European Space Agency mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the Data Processing and Analysis Consortium has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. Support was provided in part by NASA through grant number HST-GO-16743 from the Space Telescope Science Institute, which is operated by AURA, Inc., under NASA contract NAS 5-26555. A version of this article was presented as a dissertation to the Department of Astronomy and Astrophysics at The University of Chicago.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Taylor J. Hoyt.

Ethics declarations

Competing interests

The author declares no competing interests.

Peer review

Peer review information

Nature Astronomy thanks the anonymous reviewers for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Two-staged Sample Selection Procedure.

a, First, a cut is made based on the width of the distribution of TRGB magnitudes I0,TRGB determined via bootstrapping the RGB LF for each of the 25 fields. The modal TRGB magnitude for each field is plotted as a function of half the 90% confidence interval for each bootstrapped realization. The points are colored according to the \({{}^{{r}_{1}}}^{{{{\rm{HZ}}}}09}\) parameter which is defined to trace intermediate-age stellar mass. A vertical dashed line indicates the first of two cuts used to clean the sample. Only the remaining 15 fields are considered in the next panel. b, Second selection based on the asymmetry of the edge detector response (EDR) and the bootstrapped interval width. The difference between the upper (84%) and lower (16%) limits of the 68% intervals is plotted on the x-axis, the same bootstrap 90% CI is plotted on the y-axis, and the points are colored according to their field number to aid in identification. A circle of radius 0.025 mag is plotted to represent the cutoff adopted for the calibration sample. The next closest point (Field 5) is located 0.043 mag from the origin, while the furthest points are up to 0.115 mag from the origin. The SMC lies in The five fields adopted for the calibration sample cluster together and exhibit unambiguous, singularly peaked TRGB features. All plotted values are tabulated in Extended Data Table 2. More details on both sets of cuts are provided in Supplementary Fig. 2 and 3.

Extended Data Fig. 2 Maps of Intermediate-age and Young Stellar Populations in the LMC.

The Harris & Zaritsky (HZ09)67 star-formation history (SFH) maps are integrated into mass bins that represent intermediate-age (panel a) and young (panel b) stellar populations (integrals defined in Equation (3)). A black outline indicates the coverage of the OGLE-III photometric maps adopted for this study. Known star-forming structures such as the LMC’s Northern spiral arm and the 30 Dor star-forming region (R.A. ~ 85 deg, Dec. ~ -69 deg) are apparent.

Extended Data Fig. 3 Spatial distributions of young astrophysical objects and this study’s sample selection.

a, Active regions of star formation in the LMC schematically drawn over the distribution of upper RGB stars from the adopted OGLE-III catalog (its survey footprint plotted by a black outline). b, Three sets of fields plotted over the same RGB stars: the calibration sample (blue regions), the sample cut in the first set of cuts (red), and in the second set of cuts (yellow). c, Cepheids from the OGLE-IV survey30 plotted on the OGLE-IV reddening map (red dots). Intensity corresponds to E(V − I) reddening. The calibration sample is again hued and outlined (blue). d, Same as c but for HI supergiant shells (red open circles)31 e, Same as c but for the DEBs (red filled circles)18.

Extended Data Fig. 4 Determination of the on-sky orientation of the LMC using the TRGB.

a, TRGB measurements derived from all 116 OGLE-III fields. b, Same as (a) but for the 37 OGLE-III fields adopted for their singularly-peaked EDRs. c, Model predictions for the best-fit parameters Θ = 153 ± 12, i = 27 ± 3. d, Residuals. The position of the best-fit line of nodes is plotted for reference. e, Three-dimensional visualization of the best-fit plane geometry, with the negative z-axis extending in the direction of the observer. A subset (20000 sources) of the total OGLE-III sample of RGB stars is overplotted (gray points).

Extended Data Table 1 Summary of the 25 LMC Voronoi Fields
Extended Data Table 2 TRGB quality metrics for the LMC Voronoi Fields
Extended Data Table 3 Compilation of LMC-based TRGB Calibrations

Supplementary information

Supplementary Information

Supplementary Figs. 1–14, Table 1 and supplementary discussion on proper motion cleaning, sample selection, tests of geometric models and reproducibility of literature results.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hoyt, T.J. Sub-per-cent determination of the brightness at the tip of the red giant branch in the Magellanic Clouds. Nat Astron 7, 590–601 (2023). https://doi.org/10.1038/s41550-023-01913-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41550-023-01913-1

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing